The traditional single industrial chain structure is gradually evolving into the multiplex industrial chain networks. The design problem of multiplex industrial chain networks with multiple supply cycles (MICND-MSC) is studied in this paper. The impact of cross-chain supply of multiple raw materials by enterprises during the production process is considered in the problem. The mixed-integer linear programming (MILP) model of MICND-MSC is constructed and an artificial bee colony algorithm (ABC) with reinforcement learning mechanism (LDABC) is proposed to address the MICND-MSC. Heuristic methods named HMC, HMR, and PRH are designed to construct potential initial candidates for the population. The neighborhood structures for different production stages are employed in the LDABC to explore the solution space during the evolution processes. The reinforcement learning mechanism is utilized to learn empirical knowledge of neighborhood structures to guide the search process. The experimental results show that the LDABC is a potential algorithm to address the MICND-MSC.